Theorems · Theorem · probability
ProbabilityTheory.hasSum_integral_geometricMeasure
∀ {p : ↑unitInterval} {E : Type u_1} [inst : NormedAddCommGroup E] {f : ℕ → E} [inst_1 : NormedSpace ℝ E]
[CompleteSpace E],
p ≠ 0 →
MeasureTheory.Integrable f (ProbabilityTheory.geometricMeasure p) →
HasSum (fun n => ((1 - ↑p) ^ n * ↑p) • f n) (∫ (n : ℕ), f n ∂ProbabilityTheory.geometricMeasure p)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 261 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpaceproof · cited by 24,529
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- AddCommMonoidproof · cited by 12,281
- MeasureTheory.Measureproof · cited by 10,939
- Set.Elemstatement and proof · cited by 7,166
- Norm.normproof · cited by 5,413
- CompleteSpacestatement and proof · cited by 2,532
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- MeasureTheory.integralstatement and proof · cited by 1,779
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.integral_geometricMeasure'proof · cited by 0